Method of Influence Coefficients for Kinematic and Dynamic Modeling of Robotic Systems

In this paper, a summary of the method of influence coefficients for kinematic and dynamic modeling is presented and extended to kinematic trees. This method allows the decoupling of the parameters defining the system's geometry and mass properties from the time states of the generalized coordinates used to define the system, which further allows for the kinematic and dynamic models to be transformed from one set of coordinates to another in a purely algebraic manner. For a multi-input–multi-output system such as a planar or spatial robotic system, the first-order influence coefficients are matrices, while the second-order influence coefficients are arrays of matrices. This paper starts by describing the structure of these coefficients followed by a description of the algebraic operations involving these. Next, an approach to compute the kinematic influence coefficients for kinematic trees of general geometry is presented followed by a description of the computations involved in determining the inertial influence coefficients used to compute the inertial forces acting on the system. The transformation of the influence coefficients from one set of generalized coordinates to another is also shown. Finally, a planar mechanism with seven joints and two end-effectors is used to illustrate the use of the method and to convert an open-loop mechanism into a closed-loop one.